Constraint-based verification of imperative programs

work presented in the context of the European Master’s program in Computational Logic, as the partial requirement for obtaining Master of Science degree in Computational LogicThe continuous reduction in the cost of computing ever since the first days of computers has resulted in the ubiquity of computing systems today; there is no any sphere of life in the daily routine of human beings that is not directly or indirectly influenced by computer systems anymore. But this high reliance on computers has not come without a risk to the society or a challenge to computer scientists. As many computer systems of today are safety critical, it is crucial for computer scientists to make sure that computer systems, both the hardware and software components, behave correctly under all circumstances. In this study, we are interested in techniques of program verification that are aimed at ensuring the correctness of the software component. In this work, constraint programming techniques are used to device a program verification framework where constraint solvers play the role of typical verification tools. The programs considered are written in some subset of Java, and their specifications are written in some subset of Java Modeling Language(JML). In our framework, the program verification process has two principal steps: constraint generation and constraint solving. A program together with its specification is first parsed into a system of constraints. And then, the system of constraints is processed using constraint solvers so that the correctness of the original program is proved to hold, or not, based on the outcome of the constraint solving. The performance of our framework is compared with other well-known program verification tools using standard benchmarks, and our framework has performed quite well for most of the cases

Constraint-based Verification of Formation Control

Collision-free motion planning of formation of robots is an essential property to assess for safety purpose. We propose in this paper a new formal verification method based on abstract interpretation and constraint satisfaction problems to reach this goal. We consider state of the art control algorithms for formation maneuver to generate trajectories for a group of robots. Additionally, bounded uncertainties are considered to represent potential localization and measure errors. The collision-free property is formalized using the constraint satisfaction problem framework

Efficient First-Order Temporal Logic for Infinite-State Systems

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification.Comment: 16 pages, 2 figure

Abstraction of Elementary Hybrid Systems by Variable Transformation

Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safety-critical domains. Due to the non-polynomial expressions which lead to undecidable arithmetic, verification of EHSs is very hard. Existing approaches based on partition of state space or over-approximation of reachable sets suffer from state explosion or inflation of numerical errors. In this paper, we propose a symbolic abstraction approach that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all non-polynomial terms with newly introduced variables. Thus the verification of EHSs is reduced to the one of PHSs, enabling us to apply all the well-established verification techniques and tools for PHSs to EHSs. In this way, it is possible to avoid the limitations of many existing methods. We illustrate the abstraction approach and its application in safety verification of EHSs by several real world examples

Analog and Mixed Signal Verification

More and more electronic systems have components that are not purely digital. Verification of such systems is a much less developed discipline than the digital equivalents and the application of formal (mathematically complete) techniques is a nascent area. In this paper, we will discuss the nature of analog circuit design and describe the way verification is done in practice today. We will describe some “formal” approaches coming from the analog design community. We will describe some of the approaches to formal verification that have been presented in recent literature. Finally, we will mention some areas where there are opportunities for future work

Ranking Templates for Linear Loops

We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. This approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, piecewise, and lexicographic ranking functions. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin's Transposition Theorem instead of Farkas Lemma to transform the generated $\exists\forall$-constraint into an $\exists$-constraint.Comment: TACAS 201

Finite Model Finding for Parameterized Verification

In this paper we investigate to which extent a very simple and natural "reachability as deducibility" approach, originated in the research in formal methods in security, is applicable to the automated verification of large classes of infinite state and parameterized systems. The approach is based on modeling the reachability between (parameterized) states as deducibility between suitable encodings of states by formulas of first-order predicate logic. The verification of a safety property is reduced to a pure logical problem of finding a countermodel for a first-order formula. The later task is delegated then to the generic automated finite model building procedures. In this paper we first establish the relative completeness of the finite countermodel finding method (FCM) for a class of parameterized linear arrays of finite automata. The method is shown to be at least as powerful as known methods based on monotonic abstraction and symbolic backward reachability. Further, we extend the relative completeness of the approach and show that it can solve all safety verification problems which can be solved by the traditional regular model checking.Comment: 17 pages, slightly different version of the paper is submitted to TACAS 201